{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T00:00:10Z","timestamp":1758585610127,"version":"3.44.0"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032052278","type":"print"},{"value":"9783032052285","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T00:00:00Z","timestamp":1758499200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T00:00:00Z","timestamp":1758499200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-05228-5_3","type":"book-chapter","created":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:00:45Z","timestamp":1758474045000},"page":"18-27","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysing New Entropy Measures for\u00a0Tries"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9591-057X","authenticated-orcid":false,"given":"Lorenzo","family":"Carfagna","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0009-5149-2416","authenticated-orcid":false,"given":"Carlo","family":"Tosoni","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,22]]},"reference":[{"issue":"2","key":"3_CR1","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1007\/s00453-015-9969-x","volume":"74","author":"D Arroyuelo","year":"2015","unstructured":"Arroyuelo, D., Davoodi, P., Satti, S.R.: Succinct dynamic cardinal trees. Algorithmica 74(2), 742\u2013777 (2015). https:\/\/doi.org\/10.1007\/s00453-015-9969-x","journal-title":"Algorithmica"},{"issue":"4","key":"3_CR2","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/S00453-004-1146-6","volume":"43","author":"D Benoit","year":"2005","unstructured":"Benoit, D., Demaine, E.D., Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Representing trees of higher degree. Algorithmica 43(4), 275\u2013292 (2005). https:\/\/doi.org\/10.1007\/S00453-004-1146-6","journal-title":"Algorithmica"},{"key":"3_CR3","unstructured":"Carfagna, L., Tosoni, C.: Indexing tries within entropy-bounded space (2025). https:\/\/arxiv.org\/abs\/2507.02728"},{"key":"3_CR4","volume-title":"Elements of Information Theory","author":"TM Cover","year":"2006","unstructured":"Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, USA (2006)"},{"issue":"3","key":"3_CR5","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1002\/spe.4380230305","volume":"23","author":"JJ Darragh","year":"1993","unstructured":"Darragh, J.J., Cleary, J.G., Witten, I.H.: Bonsai: a compact representation of trees. Softw. Pract. Exper. 23(3), 277\u2013291 (1993). https:\/\/doi.org\/10.1002\/spe.4380230305","journal-title":"Softw. Pract. Exper."},{"key":"3_CR6","doi-asserted-by":"publisher","unstructured":"Davoodi, P., Rao, S.S.: Succinct dynamic cardinal trees with constant time operations for small alphabet. In: Ogihara, M., Tarui, J. (eds.) Theory and Applications of Models of Computation, pp. 195\u2013205. Springer Berlin Heidelberg, Berlin, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-20877-5_21","DOI":"10.1007\/978-3-642-20877-5_21"},{"key":"3_CR7","doi-asserted-by":"publisher","unstructured":"Dershowitz, N., Zaks, S.: The cycle lemma and some applications. Eur. J. Comb. 11(1), 35\u201340 (1990). https:\/\/doi.org\/10.1016\/S0195-6698(13)80053-4","DOI":"10.1016\/S0195-6698(13)80053-4"},{"issue":"2","key":"3_CR8","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1215\/S0012-7094-47-01423-3","volume":"14","author":"A Dvoretzky","year":"1947","unstructured":"Dvoretzky, A., Motzkin, T.: A problem of arrangements. Duke Math. J. 14(2), 305\u2013313 (1947). https:\/\/doi.org\/10.1215\/S0012-7094-47-01423-3","journal-title":"Duke Math. J."},{"key":"3_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/978-3-642-02927-1_38","volume-title":"Automata, Languages and Programming","author":"A Farzan","year":"2009","unstructured":"Farzan, A., Raman, R., Rao, S.S.: Universal succinct representations of trees? In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 451\u2013462. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-02927-1_38"},{"key":"3_CR10","doi-asserted-by":"publisher","unstructured":"Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Structuring labeled trees for optimal succinctness, and beyond. In: 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), 23-25 October 2005, Pittsburgh, PA, USA, Proceedings, pp. 184\u2013196. IEEE Computer Society (2005). https:\/\/doi.org\/10.1109\/SFCS.2005.69","DOI":"10.1109\/SFCS.2005.69"},{"key":"3_CR11","doi-asserted-by":"publisher","unstructured":"Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Compressing and indexing labeled trees, with applications. J. ACM 57(1), 4:1\u20134:33 (2009). https:\/\/doi.org\/10.1145\/1613676.1613680","DOI":"10.1145\/1613676.1613680"},{"key":"3_CR12","doi-asserted-by":"crossref","unstructured":"Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press (2009)","DOI":"10.1017\/CBO9780511801655"},{"key":"3_CR13","unstructured":"Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics: A Foundation for Computer Science, 2nd Ed. Addison-Wesley (1994). https:\/\/www-cs-faculty.stanford.edu\/%7Eknuth\/gkp.html"},{"key":"3_CR14","doi-asserted-by":"publisher","unstructured":"Kosolobov, D., Sivukhin, N.: Compressed multiple pattern matching. In: Pisanti, N., Pissis, S.P. (eds.) 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019, June 18-20, 2019, Pisa, Italy. LIPIcs, vol.\u00a0128, pp. 13:1\u201313:14. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2019). https:\/\/doi.org\/10.4230\/LIPICS.CPM.2019.13","DOI":"10.4230\/LIPICS.CPM.2019.13"},{"key":"3_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/11496656_5","volume-title":"Combinatorial Pattern Matching","author":"V M\u00e4kinen","year":"2005","unstructured":"M\u00e4kinen, V., Navarro, G.: Succinct suffix arrays based on run-length encoding. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 45\u201356. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11496656_5"},{"key":"3_CR16","doi-asserted-by":"crossref","unstructured":"Navarro, G.: Compact Data Structures - A Practical Approach. Cambridge University Press (2016)","DOI":"10.1017\/CBO9781316588284"},{"key":"3_CR17","doi-asserted-by":"publisher","unstructured":"Prezza, N.: On locating paths in compressed tries. In: Marx, D. (ed.) Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Virtual Conference, January 10 - 13, 2021, pp. 744\u2013760. SIAM (2021). https:\/\/doi.org\/10.1137\/1.9781611976465.47","DOI":"10.1137\/1.9781611976465.47"},{"key":"3_CR18","doi-asserted-by":"publisher","unstructured":"Prodinger, H.: Counting edges according to edge-type in $$t$$-ary trees (2022). https:\/\/doi.org\/10.48550\/arXiv.2205.13374","DOI":"10.48550\/arXiv.2205.13374"},{"key":"3_CR19","doi-asserted-by":"publisher","unstructured":"Raman, R., Raman, V., Satti, S.R.: Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Trans. Algorithms 3(4), 43\u2013es (2007). https:\/\/doi.org\/10.1145\/1290672.1290680","DOI":"10.1145\/1290672.1290680"},{"key":"3_CR20","unstructured":"Rote, G.: Binary trees having a given number of nodes with 0, 1, and 2 children. S\u00e9minaire Lotharingien de Combinatoire, B38b (1997). https:\/\/www.emis.de\/journals\/SLC\/wpapers\/s38proding.html"}],"container-title":["Lecture Notes in Computer Science","String Processing and Information Retrieval"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-05228-5_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:00:46Z","timestamp":1758474046000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-05228-5_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,22]]},"ISBN":["9783032052278","9783032052285"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-05228-5_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,22]]},"assertion":[{"value":"22 September 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SPIRE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on String Processing and Information Retrieval","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"London","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"32","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"spire2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sites.google.com\/view\/spire-2025\/home","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}